The calculations were made in R using R-Studio. The structure of the
code is essentially based on the structure of the text. The raw code is
in the file order_of_code.R. The file extended with
Markdown is order_of_code-doc.RMD and the file
order_of_code-doc.pdf is generated from it.
The code makes extensive use of the function source to
call external code. Thus, the main part of the code remains slim, well
structured and readable.
Note: The base path for rmd files is the folder in which they are
located, not the r-project. Consequently, order_of_code.R
and order_of_code-doc.RMD are both located in the root
folder of the project.
Install required packages, set some options and link the sources for the helper functions.
Remark: The current version of osmplotr has to be installed from
github using
devtools::install_github ("ropensci/osmplotr").
require(pacman) || install.packages("pacman")
## Loading required package: pacman
## [1] TRUE
pacman::p_load(dplyr, fitdistrplus, flexsurv, ggplot2, gridExtra, kableExtra,
mortAAR, nlme, osmplotr, reshape2, rgdal, HMDHFDplus, Metrics,
svMisc, tibble, tidyr, cowplot, MortalityLaws, rio,
coda, rjags, runjags, demogR, sf, rnaturalearth, readxl,
ggrepel)
## Installing package into '/Volumes/SanDisk/Nils/Library/R/arm64/4.3/library'
## (as 'lib' is unspecified)
## Warning: package 'osmplotr' is not available for this version of R
##
## A version of this package for your version of R might be available elsewhere,
## see the ideas at
## https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packages
## Warning: 'BiocManager' not available. Could not check Bioconductor.
##
## Please use `install.packages('BiocManager')` and then retry.
## Warning in p_install(package, character.only = TRUE, ...):
## Warning in library(package, lib.loc = lib.loc, character.only = TRUE,
## logical.return = TRUE, : there is no package called 'osmplotr'
## Warning in pacman::p_load(dplyr, fitdistrplus, flexsurv, ggplot2, gridExtra, : Failed to install/load:
## osmplotr
options(scipen = 999)
options(dplyr.summarise.inform = FALSE)
source("./functions/bayes_cat_poisson.R")
source("./functions/gomp_MLE.R")
source("./functions/gomp_MLE_adapted.R")
source("./functions/gomp_MLE_interval.R")
source("./functions/gomp_anthr_age.R")
source("./functions/gomp_anthr_age_r.R")
source("./functions/gomp_bayes_known_age.R")
source("./functions/gomp_known_age_r.R")
source("./functions/helper_functions.R")
source("./functions/lt_MC.R")
source("./functions/lt_MC_Gomp.R")
RNGkind("L'Ecuyer-CMRG") # conservative random number generator to avoid periodicity
Important for saving time: Decide to run extensive code anew (app. 6 h +). In addition, you can set the folder for preprocessed files.
runCodeNew <- FALSE
#runCodeNew <- TRUE
saveFileDir = "preprocessed_files"
if (saveFileDir %in% list.files(getwd()))
{}else{
dir.create(file.path(".", saveFileDir), showWarnings = FALSE )
}
## NULL
Figure 1: Exemplary life table curves generated by Gompertz functions with different \(\beta\) parameters.
source("./chapter_01_introduction/gompertz_distribution.R")
## Saving 7 x 5 in image
Figure 3: Hazard curve for HMD UK data of the year 1841.
source("./chapter_02_materials_and_methods/hazard_curve.R")
## Saving 7 x 5 in image
Figure 4: Major cemeteries in Greater London 1100–1850 used in the present study.
source("./chapter_03_data/London_places.R")
## Data (c) OpenStreetMap contributors, ODbL 1.0. https://www.openstreetmap.org/copyright
## Saving 7 x 5 in image
Table 1: Overview of included cemeteries with osteoarchaeological data.
read.table("chapter_03_data/london_cemeteries.txt", header = T, sep = "\t") %>%
knitr::kable(., caption = "Overview of included cemeteries with osteoarchaeological data.") %>%
kableExtra::kable_styling(latex_options = "HOLD_position") %>% unclass() %>% cat()
| Map.nr. | name | period | excavation.date | social.character | absolute.n | n.analysed | n….12.years | references |
|---|---|---|---|---|---|---|---|---|
| 6 | Bermondsey Abbey | 1089–1538 | 1984–1995 | monks | 208 | 201 | 201 | Dyson et al. (2011) |
| 8 | St. Mary Spital | 1120–1538 | 1991–2007 | commoners | 10,516 | 5,387 | Connell et al. (2012) | |
| NA | period 14: 1120–1200 | 347 | 329 | |||||
| NA | period 15: 1200–1250 | 510 | 470 | |||||
| NA | period 16: 1250–1400 | 1,392 | 1,361 | |||||
| NA | period 17: 1400–1539 | 526 | 467 | |||||
| 3 | St. Mary Graces | 1350–1540 | 1986–1988 | commoners | 378 | 298 | Grainger/Phillpotts (2011) | |
| 7 | New Churchyard | 1569–1739 | 2011–2015 | low status | 3,354 | 682 (category A) | 556 | Hartle et al. (2017) |
| 4 | St. Benet Sherehog | 1670–1740 | 1994–1996 | higher status | 230 | 179 | Miles et al. (2008a) | |
| 1 | St. Marylebone | 1767–1859 | 1992; 2003 | high status | 301 | 226 | Miles et al. (2008b) | |
| 2 | St. Marylebone Paddington Street north | 1772–1853 | 2012–2013 | high status | 385 | 291 | 232 | Henderson et al. (2015) |
| 9 | Chelsea Old church | 1712–1842 | 2000 | mixed | 198 | 168 | Cowie et al. (2008) | |
| 5 | St. Brides crypt | 1740–1853 | high | 216 | Scheuer, J. L. (1995); Scheuer, L. (1998) | |||
| 10 | St. Brides lower churchyard | 1770–1849 | low | 606 | 379 | Kausmally (2008) | ||
| 11 | St Mary and St Michaels burial ground | 1843–1854 | 2004–2005 | low, Irish immigrants | 760 | 705 | 284 | Henderson et al. (2013) |
| 12 | Sheens burial ground | 1763–1853 | 2006–2007 | low | 265 | 254 | 172 | Henderson et al. (2013) |
| 13 | Bow Baptist church | 1816–1853 | 2006; 2008 | villagers | 440 | 416 | 231 | Henderson et al. (2013) |
Figure 5: Population development of London, compiled from Finlay/Shearer (1986), 39 table 1; Landers (1993), 41; 179 table 5.7; Weinreb et al. (2008), 655–657.
source("./chapter_03_data/London_population.R")
grid::grid.newpage()
grid::grid.draw(rbind(london_pop1, london_pop2))
Footnote 6: Re-calculation of population increase rates of London from Razzell/Spence (2007). Calculated in ./chapter_03_data/London_population.R
knitr::kable(razz_df, caption = "Re-calculation of population increase rates of London from Razzell/Spence 2007.")%>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| date | population | rate.per.year |
|---|---|---|
| 1520 | 55000 | NA |
| 1600 | 200000 | 0.016 |
| 1650 | 400000 | 0.014 |
| 1700 | 575000 | 0.007 |
| 1750 | 675000 | 0.003 |
| 1801 | 960000 | 0.007 |
| 1851 | 2685000 | 0.021 |
Preprocessing of data used in figure 6: Estimated modal ages.
Basic statistics
The data is referenced and aggregated in
“./chapter_04_results/historical_lifetables.R”. In this file, all
records from individual preprocessing files located in
“./liftables_preprocessed/” are sourced. The corresponding
data files are stored in “./data/”.
English_Peers.R, russell.txt, Source: La Poutré/Janssen (2021), table 2
source("./chapter_04_results/historical_lifetables.R")
kable(peers_ranges, caption = "English Peers") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| parameter | modes | HDI.ranges |
|---|---|---|
| beta | 0.0613 | 0.0559-0.0660 |
| M | 58.1758 | 56.4-59.8 |
| e20 | 33.4148 | NA |
| e25 | 29.4926 | NA |
Medieval_England.R, Christ_church_monks.txt, Source: Hatcher et al. (2006), 28 table 2
kable(monks_ranges, caption = "Christ Church monks") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| parameter | modes | HDI.ranges |
|---|---|---|
| beta | 0.0461 | 0.0398-0.0523 |
| M | 52.7659 | 48.9-56.0 |
| e20 | 31.0948 | NA |
| e25 | 27.7530 | NA |
London_1728_1840.R, Mortality_bills_1728_1840.txt, Source: Roberts/Cox (2003), 304 Table 6.5; > 100 years and < 1 year collapsed
kable(london_1728_1840_ranges,
caption = "London Mortality bills 1728-1840.") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| parameter | ranges |
|---|---|
| beta | 0.0326-0.0418 |
| M | 43.3-54.8 |
kable(london_1728_1840_ranges_r,
caption = "London Mortality bills 1728-1840, corrected for population growth.") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| parameter | ranges |
|---|---|
| beta_r | 0.034-0.0507 |
| M_r | 46-64.3 |
| r | 0.002-0.019 |
London_1841_raw_all.R, London_1841_raw.txt, Source: Graham (1842), 19 table q.
kable(London_1841_ranges,
caption = "Census data for London from 1841.") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| parameter | modes | HDI.ranges |
|---|---|---|
| beta | 0.0547 | 0.0510-0.0585 |
| M | 60.4164 | 58.9-61.7 |
English_Mortality.R, wrigley_et_al_1997_england_1640-1809.txt, Source: Wrigley et al. (1997), 290 table 6.19
kable(eng_mort_ranges,
caption = "English mortality data.") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| parameter | ranges |
|---|---|
| beta | 0.0438-0.0608 |
| M | 52.2-67.4 |
HMD_UK_ranges.R
The data from the Human Mortality Database (https://mortality.org/) were retrieved with a personal account using the R package HMDHFDplus. Therefore, we only provide the processed data here.
kable(HMD_UK_ranges, caption = "Human Mortality Database UK.") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| parameter | ranges |
|---|---|
| beta | 0.05-0.0654 |
| M | 64.2-70.2 |
Extended statistics
kable(peers_result, caption = "English Peers.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh | |
|---|---|---|---|---|---|---|---|---|---|---|
| a | 1.000356 | 1.001061 | 0.0044095 | 0.0043879 | 0.0043263 | 11315.3 | 0.0000044 | 0.95 | 0.0035238 | 0.0053575 |
| b | 1.000307 | 1.000854 | 0.0609452 | 0.0609518 | 0.0612976 | 11121.9 | 0.0000244 | 0.95 | 0.0559415 | 0.0660412 |
| M | 1.000196 | 1.000696 | 58.1500750 | 58.1648975 | 58.1757927 | 20660.4 | 0.0059675 | 0.95 | 56.4492001 | 59.8036275 |
kable(monks_result, caption = "Christ Church monks.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| start | end | parameter | PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1395 | 1505 | alpha | 1.000569 | 1.001661 | 0.0102993 | 0.0102563 | 0.0100488 | 13991.9 | 0.0000096 | 0.95 | 0.0081076 | 0.0125497 |
| 1395 | 1505 | beta | 1.000498 | 1.001436 | 0.0459467 | 0.0459287 | 0.0461060 | 13623.6 | 0.0000273 | 0.95 | 0.0397953 | 0.0523389 |
| 1395 | 1505 | M | 1.000504 | 1.001504 | 52.5281106 | 52.6296486 | 52.7658924 | 15808.5 | 0.0143226 | 0.95 | 48.9344189 | 55.9631681 |
kable(london_1728_1840_result,
caption = "London Mortality bills 1728-1840.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| year | parameter | PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh |
|---|---|---|---|---|---|---|---|---|---|---|---|
| X1728 | alpha | 1.000087 | 1.000306 | 0.0146842 | 0.0146345 | 0.0145833 | 17556.5 | 0.0000101 | 0.95 | 0.0121424 | 0.0173529 |
| X1728 | beta | 1.000115 | 1.000412 | 0.0349280 | 0.0349276 | 0.0347502 | 17418.0 | 0.0000202 | 0.95 | 0.0296810 | 0.0401486 |
| X1728 | M | 1.000083 | 1.000299 | 44.6441200 | 44.8860914 | 45.5314756 | 17327.3 | 0.0224261 | 0.95 | 38.6469401 | 50.0270569 |
| X1730 | alpha | 1.000130 | 1.000390 | 0.0156561 | 0.0155984 | 0.0155550 | 17707.3 | 0.0000113 | 0.95 | 0.0127651 | 0.0186532 |
| X1730 | beta | 1.000044 | 1.000181 | 0.0325647 | 0.0325599 | 0.0325660 | 17242.0 | 0.0000212 | 0.95 | 0.0271489 | 0.0380817 |
| X1730 | M | 1.000124 | 1.000377 | 42.2325103 | 42.5795321 | 43.3073366 | 17007.1 | 0.0285150 | 0.95 | 34.7635858 | 49.1029390 |
| X1740 | alpha | 1.000404 | 1.001423 | 0.0153988 | 0.0153491 | 0.0151995 | 17959.5 | 0.0000100 | 0.95 | 0.0128421 | 0.0180871 |
| X1740 | beta | 1.000376 | 1.001376 | 0.0337368 | 0.0337428 | 0.0337806 | 17712.7 | 0.0000192 | 0.95 | 0.0286838 | 0.0387413 |
| X1740 | M | 1.000496 | 1.001609 | 43.0631632 | 43.3280277 | 43.9606200 | 17454.0 | 0.0235235 | 0.95 | 36.6700553 | 48.6880952 |
| X1750 | alpha | 1.000135 | 1.000198 | 0.0151763 | 0.0151270 | 0.0150364 | 18259.1 | 0.0000101 | 0.95 | 0.0125377 | 0.0178563 |
| X1750 | beta | 1.000114 | 1.000178 | 0.0342964 | 0.0342869 | 0.0341703 | 18177.8 | 0.0000196 | 0.95 | 0.0290894 | 0.0394288 |
| X1750 | M | 1.000179 | 1.000275 | 43.5924225 | 43.8460270 | 44.4983607 | 17767.1 | 0.0230817 | 0.95 | 37.4073951 | 49.2703888 |
| X1760 | alpha | 1.000177 | 1.000629 | 0.0145817 | 0.0145330 | 0.0143877 | 17316.9 | 0.0000100 | 0.95 | 0.0120971 | 0.0172323 |
| X1760 | beta | 1.000136 | 1.000506 | 0.0350143 | 0.0350086 | 0.0350484 | 17001.2 | 0.0000202 | 0.95 | 0.0298241 | 0.0401131 |
| X1760 | M | 1.000187 | 1.000641 | 44.8612069 | 45.0945299 | 45.4484334 | 17136.0 | 0.0220610 | 0.95 | 39.0545641 | 50.2289914 |
| X1770 | alpha | 1.000210 | 1.000234 | 0.0143004 | 0.0142472 | 0.0140950 | 17376.2 | 0.0000100 | 0.95 | 0.0117447 | 0.0168976 |
| X1770 | beta | 1.000111 | 1.000112 | 0.0356448 | 0.0356520 | 0.0357779 | 17075.8 | 0.0000206 | 0.95 | 0.0303640 | 0.0408917 |
| X1770 | M | 1.000272 | 1.000317 | 45.4735868 | 45.7082853 | 46.2765443 | 17338.6 | 0.0215703 | 0.95 | 39.8841834 | 50.8485089 |
| X1780 | alpha | 1.000514 | 1.001561 | 0.0136096 | 0.0135643 | 0.0135416 | 17117.8 | 0.0000093 | 0.95 | 0.0112683 | 0.0160201 |
| X1780 | beta | 1.000465 | 1.001440 | 0.0367597 | 0.0367653 | 0.0367765 | 16987.0 | 0.0000198 | 0.95 | 0.0317257 | 0.0418630 |
| X1780 | M | 1.000566 | 1.001711 | 46.9184820 | 47.1022825 | 47.2254317 | 17138.4 | 0.0191612 | 0.95 | 41.9217381 | 51.6370888 |
| X1790 | alpha | 1.001017 | 1.003544 | 0.0126577 | 0.0126131 | 0.0125275 | 16575.3 | 0.0000091 | 0.95 | 0.0104144 | 0.0149800 |
| X1790 | beta | 1.000983 | 1.003179 | 0.0385025 | 0.0385094 | 0.0386019 | 16305.1 | 0.0000206 | 0.95 | 0.0333766 | 0.0437012 |
| X1790 | M | 1.000966 | 1.003389 | 48.8104699 | 48.9690668 | 49.1799758 | 17098.7 | 0.0174550 | 0.95 | 44.3144300 | 53.1380827 |
| X1800 | alpha | 1.000110 | 1.000420 | 0.0116860 | 0.0116468 | 0.0115927 | 16299.7 | 0.0000084 | 0.95 | 0.0096049 | 0.0137829 |
| X1800 | beta | 1.000087 | 1.000347 | 0.0399538 | 0.0399387 | 0.0396845 | 16015.0 | 0.0000202 | 0.95 | 0.0349411 | 0.0449695 |
| X1800 | M | 1.000108 | 1.000414 | 50.7157959 | 50.8389930 | 51.1834695 | 17252.3 | 0.0153333 | 0.95 | 46.6384629 | 54.4728117 |
| X1810 | alpha | 1.000243 | 1.000527 | 0.0115193 | 0.0114800 | 0.0114383 | 15734.5 | 0.0000082 | 0.95 | 0.0095164 | 0.0135694 |
| X1810 | beta | 1.000118 | 1.000358 | 0.0383935 | 0.0383896 | 0.0384657 | 15460.0 | 0.0000197 | 0.95 | 0.0335364 | 0.0431518 |
| X1810 | M | 1.000326 | 1.000622 | 51.2962821 | 51.4292427 | 51.6215562 | 16508.4 | 0.0161901 | 0.95 | 47.0977231 | 55.2320786 |
| X1820 | alpha | 1.000052 | 1.000181 | 0.0104841 | 0.0104445 | 0.0102781 | 15011.2 | 0.0000079 | 0.95 | 0.0086351 | 0.0124260 |
| X1820 | beta | 1.000027 | 1.000124 | 0.0403826 | 0.0403829 | 0.0404617 | 14970.0 | 0.0000204 | 0.95 | 0.0354909 | 0.0452688 |
| X1820 | M | 1.000055 | 1.000187 | 53.3587767 | 53.4706305 | 53.7399168 | 16366.7 | 0.0145839 | 0.95 | 49.6763807 | 56.9584942 |
| X1830 | alpha | 1.000258 | 1.000430 | 0.0098584 | 0.0098256 | 0.0097258 | 14395.4 | 0.0000077 | 0.95 | 0.0080812 | 0.0116651 |
| X1830 | beta | 1.000286 | 1.000581 | 0.0420293 | 0.0420238 | 0.0418237 | 14224.9 | 0.0000211 | 0.95 | 0.0371298 | 0.0469784 |
| X1830 | M | 1.000236 | 1.000371 | 54.4809550 | 54.5648372 | 54.7531694 | 16267.7 | 0.0133487 | 0.95 | 51.0810043 | 57.7147665 |
| X1840 | alpha | 1.000201 | 1.000590 | 0.0103011 | 0.0102629 | 0.0101990 | 14208.6 | 0.0000081 | 0.95 | 0.0084545 | 0.0122232 |
| X1840 | beta | 1.000209 | 1.000633 | 0.0409196 | 0.0409247 | 0.0410181 | 14009.2 | 0.0000213 | 0.95 | 0.0359043 | 0.0457889 |
| X1840 | M | 1.000202 | 1.000548 | 53.6779375 | 53.7846103 | 53.9681394 | 15624.6 | 0.0146214 | 0.95 | 50.0085204 | 57.1315996 |
kable(london_1728_1840_result_r,
caption = "London Mortality bills 1728-1840, corrected for population growth.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| year | parameter | PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh |
|---|---|---|---|---|---|---|---|---|---|---|---|
| X1728 | alpha | 1.000216 | 1.000632 | 0.0117973 | 0.0117320 | 0.0118127 | 12703.3 | 0.0000126 | 0.95 | 0.0090855 | 0.0145984 |
| X1728 | beta | 1.000264 | 1.000811 | 0.0383802 | 0.0383752 | 0.0385662 | 13742.4 | 0.0000251 | 0.95 | 0.0326747 | 0.0441749 |
| X1728 | M | 1.000177 | 1.000534 | 50.6676878 | 50.8590788 | 51.5853562 | 13177.1 | 0.0252464 | 0.95 | 44.7887126 | 56.0258710 |
| X1728 | rate | 1.000032 | 1.000061 | 0.0067646 | 0.0067607 | 0.0067957 | 25886.2 | 0.0000155 | 0.95 | 0.0018885 | 0.0116701 |
| X1730 | alpha | 1.000179 | 1.000607 | 0.0143632 | 0.0142738 | 0.0140413 | 13423.4 | 0.0000148 | 0.95 | 0.0111303 | 0.0178349 |
| X1730 | beta | 1.000209 | 1.000645 | 0.0340807 | 0.0340719 | 0.0339992 | 14402.5 | 0.0000247 | 0.95 | 0.0282252 | 0.0398462 |
| X1730 | M | 1.000167 | 1.000545 | 45.1548428 | 45.5041559 | 46.1942144 | 13398.1 | 0.0340936 | 0.95 | 37.2310898 | 52.4481763 |
| X1730 | rate | 1.000100 | 1.000359 | 0.0021254 | 0.0021267 | 0.0023925 | 28508.1 | 0.0000148 | 0.95 | -0.0027647 | 0.0070247 |
| X1740 | alpha | 1.000250 | 1.000351 | 0.0143131 | 0.0142474 | 0.0141781 | 12578.6 | 0.0000142 | 0.95 | 0.0112583 | 0.0174506 |
| X1740 | beta | 1.000181 | 1.000319 | 0.0351166 | 0.0351062 | 0.0349517 | 13779.1 | 0.0000232 | 0.95 | 0.0297582 | 0.0404467 |
| X1740 | M | 1.000278 | 1.000415 | 45.4168492 | 45.6666273 | 45.9931494 | 12599.0 | 0.0307477 | 0.95 | 38.5335175 | 51.8684034 |
| X1740 | rate | 1.000068 | 1.000120 | 0.0016517 | 0.0016515 | 0.0015142 | 25567.8 | 0.0000156 | 0.95 | -0.0031950 | 0.0065573 |
| X1750 | alpha | 1.000044 | 1.000069 | 0.0122439 | 0.0121749 | 0.0120834 | 13261.9 | 0.0000125 | 0.95 | 0.0094963 | 0.0150957 |
| X1750 | beta | 1.000071 | 1.000205 | 0.0376537 | 0.0376479 | 0.0373656 | 14801.1 | 0.0000236 | 0.95 | 0.0320020 | 0.0432862 |
| X1750 | M | 1.000031 | 1.000056 | 49.7546558 | 49.9590937 | 50.2151068 | 13705.5 | 0.0254226 | 0.95 | 43.7054776 | 55.2902303 |
| X1750 | rate | 1.000077 | 1.000111 | 0.0067105 | 0.0067114 | 0.0065398 | 27317.4 | 0.0000151 | 0.95 | 0.0018180 | 0.0115565 |
| X1760 | alpha | 1.000225 | 1.000700 | 0.0116585 | 0.0115897 | 0.0114879 | 12463.7 | 0.0000123 | 0.95 | 0.0090429 | 0.0144036 |
| X1760 | beta | 1.000110 | 1.000420 | 0.0385112 | 0.0385024 | 0.0386022 | 13804.0 | 0.0000244 | 0.95 | 0.0328832 | 0.0441388 |
| X1760 | M | 1.000236 | 1.000723 | 50.9671802 | 51.1574788 | 51.4559256 | 12906.8 | 0.0247727 | 0.95 | 45.4374663 | 56.3675483 |
| X1760 | rate | 1.000227 | 1.000754 | 0.0069377 | 0.0069444 | 0.0071785 | 25388.2 | 0.0000156 | 0.95 | 0.0020562 | 0.0118077 |
| X1770 | alpha | 1.000913 | 1.002565 | 0.0119572 | 0.0118855 | 0.0116788 | 12401.3 | 0.0000128 | 0.95 | 0.0092493 | 0.0148011 |
| X1770 | beta | 1.000842 | 1.002526 | 0.0385160 | 0.0385119 | 0.0385913 | 13729.2 | 0.0000249 | 0.95 | 0.0328861 | 0.0442661 |
| X1770 | M | 1.000933 | 1.002591 | 50.3026157 | 50.5009459 | 50.9360513 | 12779.1 | 0.0255623 | 0.95 | 44.5382288 | 55.7354351 |
| X1770 | rate | 1.000327 | 1.001024 | 0.0054059 | 0.0053991 | 0.0053967 | 26694.8 | 0.0000153 | 0.95 | 0.0005155 | 0.0103390 |
| X1780 | alpha | 1.000024 | 1.000080 | 0.0098947 | 0.0098375 | 0.0097623 | 12144.8 | 0.0000109 | 0.95 | 0.0076036 | 0.0122621 |
| X1780 | beta | 1.000089 | 1.000332 | 0.0416234 | 0.0416156 | 0.0412466 | 13529.3 | 0.0000249 | 0.95 | 0.0357590 | 0.0470951 |
| X1780 | M | 1.000009 | 1.000034 | 54.5099445 | 54.6330090 | 54.9472107 | 13234.3 | 0.0205386 | 0.95 | 49.7839622 | 58.9932689 |
| X1780 | rate | 1.000029 | 1.000052 | 0.0101105 | 0.0101157 | 0.0102186 | 23262.7 | 0.0000163 | 0.95 | 0.0051865 | 0.0149529 |
| X1790 | alpha | 1.000780 | 1.002619 | 0.0074628 | 0.0074099 | 0.0072730 | 12511.4 | 0.0000086 | 0.95 | 0.0056365 | 0.0093699 |
| X1790 | beta | 1.000634 | 1.002266 | 0.0465156 | 0.0465133 | 0.0464524 | 13814.5 | 0.0000257 | 0.95 | 0.0405791 | 0.0524046 |
| X1790 | M | 1.000594 | 1.002037 | 59.3920496 | 59.4676688 | 59.6465203 | 15210.4 | 0.0154250 | 0.95 | 55.6352570 | 63.0795140 |
| X1790 | rate | 1.000364 | 1.001370 | 0.0165769 | 0.0165808 | 0.0166141 | 24083.9 | 0.0000160 | 0.95 | 0.0116026 | 0.0213767 |
| X1800 | alpha | 1.000673 | 1.001733 | 0.0067061 | 0.0066571 | 0.0065314 | 12303.3 | 0.0000078 | 0.95 | 0.0050738 | 0.0084373 |
| X1800 | beta | 1.000450 | 1.001205 | 0.0482926 | 0.0482882 | 0.0482750 | 13472.8 | 0.0000254 | 0.95 | 0.0425605 | 0.0540970 |
| X1800 | M | 1.000481 | 1.001391 | 60.9494935 | 61.0079704 | 61.2925933 | 16004.8 | 0.0138784 | 0.95 | 57.4654475 | 64.3420718 |
| X1800 | rate | 1.000147 | 1.000554 | 0.0172842 | 0.0172863 | 0.0173351 | 24114.8 | 0.0000161 | 0.95 | 0.0123533 | 0.0221326 |
| X1810 | alpha | 1.000778 | 1.002825 | 0.0061205 | 0.0060764 | 0.0060231 | 11885.0 | 0.0000073 | 0.95 | 0.0046308 | 0.0077169 |
| X1810 | beta | 1.000722 | 1.002651 | 0.0477278 | 0.0477231 | 0.0477969 | 12935.3 | 0.0000252 | 0.95 | 0.0421088 | 0.0533294 |
| X1810 | M | 1.000533 | 1.001967 | 63.1111594 | 63.1645788 | 63.3883652 | 15759.0 | 0.0139295 | 0.95 | 59.6818113 | 66.5370162 |
| X1810 | rate | 1.000355 | 1.001232 | 0.0188379 | 0.0188404 | 0.0189439 | 21465.1 | 0.0000169 | 0.95 | 0.0139210 | 0.0236200 |
| X1820 | alpha | 1.000095 | 1.000132 | 0.0055976 | 0.0055572 | 0.0054458 | 11229.6 | 0.0000070 | 0.95 | 0.0041772 | 0.0070725 |
| X1820 | beta | 1.000042 | 1.000144 | 0.0497736 | 0.0497549 | 0.0494675 | 11848.9 | 0.0000269 | 0.95 | 0.0440723 | 0.0555463 |
| X1820 | M | 1.000089 | 1.000100 | 63.9900524 | 64.0294417 | 64.0859524 | 15792.1 | 0.0130000 | 0.95 | 60.7385660 | 67.1324448 |
| X1820 | rate | 1.000054 | 1.000169 | 0.0184286 | 0.0184243 | 0.0183352 | 20638.3 | 0.0000173 | 0.95 | 0.0136164 | 0.0233407 |
| X1830 | alpha | 1.000685 | 1.002323 | 0.0055328 | 0.0054915 | 0.0053316 | 10784.7 | 0.0000071 | 0.95 | 0.0041241 | 0.0069785 |
| X1830 | beta | 1.000541 | 1.001972 | 0.0507604 | 0.0507524 | 0.0506613 | 11479.7 | 0.0000273 | 0.95 | 0.0450068 | 0.0564989 |
| X1830 | M | 1.000452 | 1.001586 | 63.7527679 | 63.7940673 | 63.8373687 | 14596.3 | 0.0130407 | 0.95 | 60.6000558 | 66.7627670 |
| X1830 | rate | 1.000340 | 1.001284 | 0.0170084 | 0.0170011 | 0.0170444 | 20042.5 | 0.0000176 | 0.95 | 0.0121792 | 0.0219144 |
| X1840 | alpha | 1.000307 | 1.001096 | 0.0054664 | 0.0054244 | 0.0053739 | 11068.3 | 0.0000069 | 0.95 | 0.0040888 | 0.0069308 |
| X1840 | beta | 1.000429 | 1.001483 | 0.0504923 | 0.0504880 | 0.0504433 | 12336.9 | 0.0000266 | 0.95 | 0.0445658 | 0.0561736 |
| X1840 | M | 1.000118 | 1.000460 | 64.1209693 | 64.1581002 | 64.3153799 | 15983.6 | 0.0125993 | 0.95 | 61.0149913 | 67.2673873 |
| X1840 | rate | 1.000057 | 1.000244 | 0.0185439 | 0.0185336 | 0.0183673 | 20908.7 | 0.0000172 | 0.95 | 0.0136249 | 0.0233586 |
kable(London_1841_result,
caption = "Census data for London from 1841.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh | |
|---|---|---|---|---|---|---|---|---|---|---|
| a | 1.000227 | 1.000481 | 0.0045780 | 0.0045654 | 0.0045126 | 15366.4 | 0.0000030 | 0.95 | 0.0038745 | 0.0053284 |
| b | 1.000173 | 1.000361 | 0.0547652 | 0.0547581 | 0.0546507 | 15261.7 | 0.0000155 | 0.95 | 0.0510256 | 0.0585294 |
| M | 1.000098 | 1.000288 | 60.3512664 | 60.3640713 | 60.4164328 | 26323.3 | 0.0044223 | 0.95 | 58.9378882 | 61.7484732 |
kable(eng_mort_result, caption = "English mortality data.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| year | parameter | PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh |
|---|---|---|---|---|---|---|---|---|---|---|---|
| X1640 | alpha | 1.000116 | 1.000213 | 0.0109640 | 0.0109440 | 0.0108724 | 20086.8 | 0.0000055 | 0.95 | 0.0094508 | 0.0125183 |
| X1640 | beta | 1.000128 | 1.000269 | 0.0473794 | 0.0473646 | 0.0471615 | 19457.0 | 0.0000160 | 0.95 | 0.0430271 | 0.0517521 |
| X1640 | M | 1.000098 | 1.000168 | 55.8790864 | 55.9257645 | 56.0762781 | 22766.9 | 0.0074788 | 0.95 | 53.6542245 | 58.0607633 |
| X1650 | alpha | 1.000196 | 1.000699 | 0.0086495 | 0.0086305 | 0.0086386 | 17477.0 | 0.0000050 | 0.95 | 0.0073694 | 0.0099516 |
| X1650 | beta | 1.000238 | 1.000818 | 0.0534298 | 0.0534191 | 0.0532174 | 17097.8 | 0.0000176 | 0.95 | 0.0488730 | 0.0579356 |
| X1650 | M | 1.000122 | 1.000456 | 59.0892102 | 59.1180884 | 59.1222939 | 22875.6 | 0.0058105 | 0.95 | 57.3707403 | 60.8059797 |
| X1660 | alpha | 1.000538 | 1.001899 | 0.0091323 | 0.0091133 | 0.0090836 | 17736.5 | 0.0000051 | 0.95 | 0.0078190 | 0.0104985 |
| X1660 | beta | 1.000442 | 1.001588 | 0.0507107 | 0.0507012 | 0.0506517 | 17263.0 | 0.0000172 | 0.95 | 0.0463039 | 0.0551739 |
| X1660 | M | 1.000484 | 1.001711 | 58.8100849 | 58.8427992 | 58.8427140 | 22595.3 | 0.0063824 | 0.95 | 56.9061034 | 60.6611103 |
| X1670 | alpha | 1.000280 | 1.000678 | 0.0109726 | 0.0109471 | 0.0109033 | 20090.3 | 0.0000056 | 0.95 | 0.0094600 | 0.0125515 |
| X1670 | beta | 1.000338 | 1.000812 | 0.0444972 | 0.0445019 | 0.0446316 | 19399.7 | 0.0000157 | 0.95 | 0.0402542 | 0.0488448 |
| X1670 | M | 1.000211 | 1.000529 | 56.4443366 | 56.5061422 | 56.5992418 | 22544.4 | 0.0083487 | 0.95 | 53.9239107 | 58.8183187 |
| X1680 | alpha | 1.000560 | 1.001531 | 0.0134499 | 0.0134251 | 0.0133309 | 22339.5 | 0.0000061 | 0.95 | 0.0116869 | 0.0152420 |
| X1680 | beta | 1.000479 | 1.001399 | 0.0435646 | 0.0435605 | 0.0437501 | 21337.1 | 0.0000151 | 0.95 | 0.0392159 | 0.0478531 |
| X1680 | M | 1.000597 | 1.001611 | 51.9412993 | 52.0117614 | 52.1884363 | 23152.8 | 0.0091727 | 0.95 | 49.1667363 | 54.6014009 |
| X1690 | alpha | 1.000203 | 1.000424 | 0.0100036 | 0.0099815 | 0.0099278 | 19068.4 | 0.0000053 | 0.95 | 0.0085828 | 0.0114492 |
| X1690 | beta | 1.000217 | 1.000487 | 0.0457255 | 0.0457144 | 0.0457837 | 18458.1 | 0.0000160 | 0.95 | 0.0414631 | 0.0499716 |
| X1690 | M | 1.000156 | 1.000323 | 58.2265512 | 58.2748183 | 58.3311613 | 22552.3 | 0.0076819 | 0.95 | 55.9044003 | 60.4191960 |
| X1700 | alpha | 1.000247 | 1.000813 | 0.0097904 | 0.0097696 | 0.0097670 | 19048.9 | 0.0000052 | 0.95 | 0.0083976 | 0.0112137 |
| X1700 | beta | 1.000228 | 1.000792 | 0.0469162 | 0.0469091 | 0.0468449 | 18524.9 | 0.0000160 | 0.95 | 0.0426635 | 0.0512282 |
| X1700 | M | 1.000210 | 1.000697 | 58.3940436 | 58.4388608 | 58.4010030 | 22362.5 | 0.0073779 | 0.95 | 56.2165699 | 60.5292073 |
| X1710 | alpha | 1.000629 | 1.002202 | 0.0076344 | 0.0076175 | 0.0075883 | 16583.9 | 0.0000046 | 0.95 | 0.0064833 | 0.0088178 |
| X1710 | beta | 1.000810 | 1.002798 | 0.0547320 | 0.0547184 | 0.0547561 | 16149.3 | 0.0000181 | 0.95 | 0.0502213 | 0.0592441 |
| X1710 | M | 1.000354 | 1.001230 | 61.0059909 | 61.0278089 | 61.0396872 | 23904.2 | 0.0053119 | 0.95 | 59.3643989 | 62.5807876 |
| X1720 | alpha | 1.000438 | 1.001584 | 0.0080028 | 0.0079824 | 0.0079301 | 17173.5 | 0.0000047 | 0.95 | 0.0068173 | 0.0092105 |
| X1720 | beta | 1.000453 | 1.001645 | 0.0560063 | 0.0560001 | 0.0558861 | 16622.0 | 0.0000179 | 0.95 | 0.0514205 | 0.0604697 |
| X1720 | M | 1.000297 | 1.001094 | 59.7548666 | 59.7785061 | 59.8227855 | 23615.5 | 0.0051845 | 0.95 | 58.1648789 | 61.2877274 |
| X1730 | alpha | 1.000128 | 1.000485 | 0.0067962 | 0.0067781 | 0.0067500 | 15125.2 | 0.0000045 | 0.95 | 0.0057413 | 0.0078882 |
| X1730 | beta | 1.000132 | 1.000481 | 0.0561362 | 0.0561233 | 0.0561525 | 14537.5 | 0.0000193 | 0.95 | 0.0516431 | 0.0607418 |
| X1730 | M | 1.000086 | 1.000325 | 62.6345173 | 62.6558894 | 62.6742840 | 23395.6 | 0.0050475 | 0.95 | 61.1122439 | 64.1406077 |
| X1740 | alpha | 1.000185 | 1.000678 | 0.0067863 | 0.0067674 | 0.0067507 | 15383.6 | 0.0000045 | 0.95 | 0.0057019 | 0.0078702 |
| X1740 | beta | 1.000260 | 1.000953 | 0.0566936 | 0.0566911 | 0.0568096 | 15043.4 | 0.0000191 | 0.95 | 0.0520709 | 0.0612724 |
| X1740 | M | 1.000063 | 1.000245 | 62.4655115 | 62.4849711 | 62.4345863 | 22893.7 | 0.0051037 | 0.95 | 60.9419302 | 63.9688404 |
| X1750 | alpha | 1.000389 | 1.001407 | 0.0053793 | 0.0053645 | 0.0053635 | 13451.8 | 0.0000040 | 0.95 | 0.0044682 | 0.0062959 |
| X1750 | beta | 1.000443 | 1.001627 | 0.0595510 | 0.0595305 | 0.0594825 | 12966.5 | 0.0000210 | 0.95 | 0.0548610 | 0.0642515 |
| X1750 | M | 1.000167 | 1.000607 | 65.4071998 | 65.4213962 | 65.4642394 | 24607.7 | 0.0044311 | 0.95 | 64.0354191 | 66.7582250 |
| X1760 | alpha | 1.000180 | 1.000387 | 0.0080565 | 0.0080378 | 0.0079359 | 17802.8 | 0.0000047 | 0.95 | 0.0068516 | 0.0092887 |
| X1760 | beta | 1.000187 | 1.000346 | 0.0488550 | 0.0488417 | 0.0488743 | 16840.4 | 0.0000169 | 0.95 | 0.0445037 | 0.0531121 |
| X1760 | M | 1.000119 | 1.000328 | 61.9016665 | 61.9336352 | 62.0050035 | 23618.5 | 0.0063598 | 0.95 | 59.9327761 | 63.7618010 |
| X1770 | alpha | 1.000469 | 1.001234 | 0.0067654 | 0.0067476 | 0.0066997 | 14881.8 | 0.0000045 | 0.95 | 0.0057073 | 0.0078687 |
| X1770 | beta | 1.000501 | 1.001341 | 0.0538935 | 0.0538804 | 0.0536262 | 14373.8 | 0.0000192 | 0.95 | 0.0494452 | 0.0584665 |
| X1770 | M | 1.000270 | 1.000709 | 63.5277738 | 63.5489910 | 63.4921572 | 22585.6 | 0.0054864 | 0.95 | 61.9173469 | 65.1383522 |
| X1780 | alpha | 1.000347 | 1.001235 | 0.0066384 | 0.0066225 | 0.0066110 | 15713.1 | 0.0000043 | 0.95 | 0.0055976 | 0.0076907 |
| X1780 | beta | 1.000349 | 1.001303 | 0.0570824 | 0.0570677 | 0.0571475 | 15127.7 | 0.0000188 | 0.95 | 0.0526292 | 0.0616896 |
| X1780 | M | 1.000195 | 1.000710 | 62.7166530 | 62.7352113 | 62.7235429 | 24154.0 | 0.0048243 | 0.95 | 61.2201635 | 64.1540268 |
| X1790 | alpha | 1.000180 | 1.000376 | 0.0058127 | 0.0057951 | 0.0057825 | 13899.0 | 0.0000042 | 0.95 | 0.0048677 | 0.0068164 |
| X1790 | beta | 1.000229 | 1.000478 | 0.0580897 | 0.0580826 | 0.0579337 | 13447.1 | 0.0000206 | 0.95 | 0.0533856 | 0.0627649 |
| X1790 | M | 1.000055 | 1.000174 | 64.6577738 | 64.6756380 | 64.7246120 | 23430.8 | 0.0047208 | 0.95 | 63.2361972 | 66.0657933 |
| X1800 | alpha | 1.000697 | 1.002167 | 0.0046142 | 0.0045977 | 0.0045567 | 12391.5 | 0.0000037 | 0.95 | 0.0038253 | 0.0054317 |
| X1800 | beta | 1.000709 | 1.002222 | 0.0608363 | 0.0608357 | 0.0608310 | 11940.3 | 0.0000219 | 0.95 | 0.0561091 | 0.0654678 |
| X1800 | M | 1.000239 | 1.000822 | 67.4325112 | 67.4451148 | 67.4486965 | 26907.8 | 0.0039816 | 0.95 | 66.1359322 | 68.6958522 |
kable(HMD_UK_result, caption = "Human Mortality Database UK.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| year | parameter | PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh |
|---|---|---|---|---|---|---|---|---|---|---|---|
| X1841 | alpha | 1.000163 | 1.000417 | 0.0036316 | 0.0036148 | 0.0035704 | 13786.9 | 0.0000032 | 0.95 | 0.0029186 | 0.0043694 |
| X1841 | beta | 1.000156 | 1.000468 | 0.0519888 | 0.0519880 | 0.0522191 | 13557.1 | 0.0000185 | 0.95 | 0.0476828 | 0.0561015 |
| X1841 | M | 1.000083 | 1.000148 | 66.2542881 | 66.2748935 | 66.3111134 | 25227.7 | 0.0056085 | 0.95 | 64.4997322 | 67.9878895 |
| X1845 | alpha | 1.000079 | 1.000297 | 0.0042938 | 0.0042780 | 0.0042669 | 14758.1 | 0.0000036 | 0.95 | 0.0034647 | 0.0051540 |
| X1845 | beta | 1.000067 | 1.000247 | 0.0498996 | 0.0498859 | 0.0500069 | 14606.7 | 0.0000180 | 0.95 | 0.0455985 | 0.0541474 |
| X1845 | M | 1.000065 | 1.000255 | 64.2120906 | 64.2353737 | 64.2258466 | 24443.1 | 0.0062539 | 0.95 | 62.2412879 | 66.0782225 |
| X1850 | alpha | 1.000973 | 1.003549 | 0.0037558 | 0.0037391 | 0.0036783 | 13963.2 | 0.0000033 | 0.95 | 0.0030110 | 0.0045196 |
| X1850 | beta | 1.000868 | 1.003159 | 0.0517607 | 0.0517548 | 0.0515669 | 13902.2 | 0.0000185 | 0.95 | 0.0475374 | 0.0561228 |
| X1850 | M | 1.000670 | 1.002447 | 65.7445767 | 65.7656894 | 65.8470383 | 24788.4 | 0.0057544 | 0.95 | 63.9683713 | 67.5152044 |
| X1855 | alpha | 1.000156 | 1.000325 | 0.0034310 | 0.0034165 | 0.0034148 | 13071.2 | 0.0000031 | 0.95 | 0.0027387 | 0.0041407 |
| X1855 | beta | 1.000111 | 1.000252 | 0.0533405 | 0.0533264 | 0.0532089 | 12901.9 | 0.0000193 | 0.95 | 0.0489858 | 0.0575821 |
| X1855 | M | 1.000055 | 1.000176 | 66.5070750 | 66.5214941 | 66.5377049 | 24496.9 | 0.0055156 | 0.95 | 64.7810996 | 68.1628553 |
| X1860 | alpha | 1.000103 | 1.000169 | 0.0034785 | 0.0034615 | 0.0034062 | 13432.3 | 0.0000031 | 0.95 | 0.0027794 | 0.0041924 |
| X1860 | beta | 1.000118 | 1.000200 | 0.0532621 | 0.0532640 | 0.0532106 | 13350.6 | 0.0000189 | 0.95 | 0.0490210 | 0.0575846 |
| X1860 | M | 1.000016 | 1.000032 | 66.2956647 | 66.3134949 | 66.3500169 | 24949.1 | 0.0054798 | 0.95 | 64.5756127 | 67.9675086 |
| X1865 | alpha | 1.000093 | 1.000333 | 0.0035991 | 0.0035837 | 0.0035330 | 13810.1 | 0.0000031 | 0.95 | 0.0028932 | 0.0043267 |
| X1865 | beta | 1.000108 | 1.000353 | 0.0530530 | 0.0530491 | 0.0530859 | 13658.1 | 0.0000185 | 0.95 | 0.0488013 | 0.0572954 |
| X1865 | M | 1.000045 | 1.000177 | 65.7780212 | 65.7953467 | 65.8802464 | 25507.4 | 0.0054316 | 0.95 | 64.0717897 | 67.4665740 |
| X1870 | alpha | 1.000077 | 1.000191 | 0.0035027 | 0.0034908 | 0.0034765 | 13760.3 | 0.0000030 | 0.95 | 0.0028292 | 0.0042127 |
| X1870 | beta | 1.000110 | 1.000242 | 0.0536849 | 0.0536587 | 0.0535650 | 13616.9 | 0.0000184 | 0.95 | 0.0495385 | 0.0579499 |
| X1870 | M | 1.000013 | 1.000070 | 65.9071237 | 65.9205478 | 65.8577523 | 25746.8 | 0.0052524 | 0.95 | 64.2645935 | 67.5678728 |
| X1875 | alpha | 1.000092 | 1.000343 | 0.0030605 | 0.0030478 | 0.0030211 | 12815.0 | 0.0000028 | 0.95 | 0.0024475 | 0.0036823 |
| X1875 | beta | 1.000131 | 1.000471 | 0.0568401 | 0.0568279 | 0.0568980 | 12685.7 | 0.0000193 | 0.95 | 0.0526071 | 0.0611415 |
| X1875 | M | 1.000031 | 1.000141 | 66.4668857 | 66.4785272 | 66.5086127 | 26537.0 | 0.0047162 | 0.95 | 64.9506366 | 67.9602202 |
| X1880 | alpha | 1.000119 | 1.000291 | 0.0027376 | 0.0027242 | 0.0026867 | 12292.1 | 0.0000026 | 0.95 | 0.0021904 | 0.0033047 |
| X1880 | beta | 1.000171 | 1.000388 | 0.0580794 | 0.0580802 | 0.0580583 | 12275.9 | 0.0000195 | 0.95 | 0.0538930 | 0.0623071 |
| X1880 | M | 1.000016 | 1.000046 | 67.6639684 | 67.6752899 | 67.6594434 | 26763.5 | 0.0045057 | 0.95 | 66.2138218 | 69.0997903 |
| X1885 | alpha | 1.000329 | 1.000699 | 0.0024297 | 0.0024169 | 0.0023954 | 11472.9 | 0.0000024 | 0.95 | 0.0019319 | 0.0029532 |
| X1885 | beta | 1.000279 | 1.000617 | 0.0605593 | 0.0605577 | 0.0605172 | 11375.3 | 0.0000207 | 0.95 | 0.0561612 | 0.0648427 |
| X1885 | M | 1.000124 | 1.000309 | 68.1749533 | 68.1842585 | 68.1928238 | 26834.9 | 0.0042250 | 0.95 | 66.8018933 | 69.5153058 |
| X1890 | alpha | 1.000121 | 1.000451 | 0.0024118 | 0.0023997 | 0.0023802 | 11867.7 | 0.0000024 | 0.95 | 0.0019247 | 0.0029285 |
| X1890 | beta | 1.000146 | 1.000531 | 0.0614665 | 0.0614588 | 0.0613662 | 11669.1 | 0.0000205 | 0.95 | 0.0571518 | 0.0657954 |
| X1890 | M | 1.000045 | 1.000148 | 67.7519542 | 67.7613179 | 67.8037905 | 28081.6 | 0.0040695 | 0.95 | 66.4069818 | 69.0759956 |
| X1895 | alpha | 1.000328 | 1.001210 | 0.0019825 | 0.0019735 | 0.0019634 | 10586.6 | 0.0000021 | 0.95 | 0.0015598 | 0.0024219 |
| X1895 | beta | 1.000267 | 1.000994 | 0.0637922 | 0.0637712 | 0.0636859 | 10594.5 | 0.0000217 | 0.95 | 0.0594245 | 0.0681856 |
| X1895 | M | 1.000224 | 1.000819 | 69.4924393 | 69.4994274 | 69.5249671 | 28489.7 | 0.0038280 | 0.95 | 68.2103261 | 70.7410684 |
| X1900 | alpha | 1.000051 | 1.000194 | 0.0017882 | 0.0017794 | 0.0017686 | 10113.1 | 0.0000020 | 0.95 | 0.0013975 | 0.0021792 |
| X1900 | beta | 1.000061 | 1.000247 | 0.0653147 | 0.0653019 | 0.0653664 | 10036.7 | 0.0000222 | 0.95 | 0.0609626 | 0.0696771 |
| X1900 | M | 1.000007 | 1.000020 | 70.1656919 | 70.1713832 | 70.1615274 | 28126.0 | 0.0036879 | 0.95 | 68.9548389 | 71.3801825 |
The data is mainly hard coded in the file ./chapter_04_results/Wellcome_DB.R.
Only St. Bride’s crypt is excluded but available from the Museum of London upon request. For general information: https://www.museumoflondon.org.uk go for: Collections > Archaeology at the Museum of London > Wellcome Osteological Research Database > St. Bride’s Church Fleet Street. If runCodeNew == TRUE the file ./lifetables_processing/stbrides_crypt.R will ask for the location of the retrieved dataset (Excel sheet) and process the data. In any other case pre-processed data will be loaded.
source("./lifetables_processing/stbrides_crypt.R")
source("./chapter_04_results/Wellcome_DB.R")
kable(wellcome_result, caption = "London cemeteries data.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| cemetery | start | end | parameter | PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bermondsey Abbey | 1089 | 1538 | alpha | 1.000095 | 1.000352 | 0.0119872 | 0.0118695 | 0.0117349 | 26882.4 | 0.0000115 | 0.95 | 0.0084108 | 0.0157410 |
| Bermondsey Abbey | 1089 | 1538 | beta | 1.000115 | 1.000319 | 0.0410531 | 0.0410516 | 0.0413654 | 23098.5 | 0.0000312 | 0.95 | 0.0318561 | 0.0503895 |
| Bermondsey Abbey | 1089 | 1538 | M | 1.000071 | 1.000266 | 41.8366810 | 42.1437778 | 42.5664355 | 29309.6 | 0.0207896 | 0.95 | 34.6719658 | 48.4310632 |
| St. Mary Graces | 1350 | 1540 | alpha | 1.000196 | 1.000732 | 0.0197808 | 0.0196850 | 0.0195223 | 35662.0 | 0.0000118 | 0.95 | 0.0154857 | 0.0241619 |
| St. Mary Graces | 1350 | 1540 | beta | 1.000244 | 1.000894 | 0.0346722 | 0.0346636 | 0.0349129 | 29450.8 | 0.0000239 | 0.95 | 0.0266567 | 0.0427213 |
| St. Mary Graces | 1350 | 1540 | M | 1.000288 | 1.000951 | 27.6620555 | 28.2853721 | 29.0829030 | 31343.0 | 0.0275212 | 0.95 | 17.7908628 | 36.1544161 |
| St. Mary Hospital, 1120-1200 | 1120 | 1200 | alpha | 1.000021 | 1.000058 | 0.0249328 | 0.0248411 | 0.0247596 | 47240.6 | 0.0000108 | 0.95 | 0.0203838 | 0.0295337 |
| St. Mary Hospital, 1120-1200 | 1120 | 1200 | beta | 1.000010 | 1.000041 | 0.0363031 | 0.0363142 | 0.0366087 | 42155.0 | 0.0000184 | 0.95 | 0.0288655 | 0.0437148 |
| St. Mary Hospital, 1120-1200 | 1120 | 1200 | M | 1.000014 | 1.000048 | 21.9000883 | 22.4278307 | 23.6171674 | 41316.5 | 0.0217592 | 0.95 | 12.9358328 | 29.6933479 |
| St. Mary Hospital, 1200-1250 | 1200 | 1250 | alpha | 1.000142 | 1.000479 | 0.0299501 | 0.0298832 | 0.0296347 | 50227.8 | 0.0000103 | 0.95 | 0.0254561 | 0.0345077 |
| St. Mary Hospital, 1200-1250 | 1200 | 1250 | beta | 1.000145 | 1.000390 | 0.0356927 | 0.0356959 | 0.0355017 | 44544.0 | 0.0000163 | 0.95 | 0.0288836 | 0.0423855 |
| St. Mary Hospital, 1200-1250 | 1200 | 1250 | M | 1.000138 | 1.000388 | 16.4726206 | 16.9685941 | 17.8228768 | 43773.7 | 0.0209091 | 0.95 | 7.6941741 | 24.3391668 |
| St. Mary Hospital, 1250-1400 | 1250 | 1400 | alpha | 1.000058 | 1.000230 | 0.0183232 | 0.0182986 | 0.0182568 | 30711.1 | 0.0000060 | 0.95 | 0.0162397 | 0.0203837 |
| St. Mary Hospital, 1250-1400 | 1250 | 1400 | beta | 1.000039 | 1.000160 | 0.0580756 | 0.0580643 | 0.0577145 | 27569.9 | 0.0000162 | 0.95 | 0.0529190 | 0.0634424 |
| St. Mary Hospital, 1250-1400 | 1250 | 1400 | M | 1.000056 | 1.000226 | 31.8403051 | 31.8802975 | 31.9815271 | 32452.4 | 0.0050096 | 0.95 | 30.0460798 | 33.5688087 |
| St. Mary Hospital, 1400-1539 | 1400 | 1539 | alpha | 1.000184 | 1.000413 | 0.0262455 | 0.0261845 | 0.0258468 | 45106.6 | 0.0000098 | 0.95 | 0.0222297 | 0.0303974 |
| St. Mary Hospital, 1400-1539 | 1400 | 1539 | beta | 1.000202 | 1.000384 | 0.0374668 | 0.0374646 | 0.0373648 | 37992.2 | 0.0000178 | 0.95 | 0.0307176 | 0.0443176 |
| St. Mary Hospital, 1400-1539 | 1400 | 1539 | M | 1.000255 | 1.000509 | 21.1562579 | 21.5422484 | 22.2118499 | 38394.6 | 0.0188420 | 0.95 | 13.7317283 | 27.8355824 |
| New Churchyard | 1569 | 1739 | alpha | 1.000100 | 1.000375 | 0.0257447 | 0.0256826 | 0.0256229 | 40693.9 | 0.0000097 | 0.95 | 0.0219664 | 0.0296497 |
| New Churchyard | 1569 | 1739 | beta | 1.000143 | 1.000447 | 0.0365472 | 0.0365523 | 0.0364771 | 33659.4 | 0.0000185 | 0.95 | 0.0298776 | 0.0431955 |
| New Churchyard | 1569 | 1739 | M | 1.000167 | 1.000489 | 21.2258180 | 21.6422371 | 22.4873708 | 34065.6 | 0.0202506 | 0.95 | 13.6829257 | 27.9012158 |
| St. Benet Sherehog | 1670 | 1740 | alpha | 1.000103 | 1.000388 | 0.0159324 | 0.0158024 | 0.0157241 | 35332.7 | 0.0000126 | 0.95 | 0.0114989 | 0.0206750 |
| St. Benet Sherehog | 1670 | 1740 | beta | 1.000166 | 1.000541 | 0.0354819 | 0.0354675 | 0.0352938 | 29914.9 | 0.0000268 | 0.95 | 0.0265131 | 0.0446216 |
| St. Benet Sherehog | 1670 | 1740 | M | 1.000123 | 1.000414 | 34.0694974 | 34.7174821 | 36.0672253 | 33191.8 | 0.0286473 | 0.95 | 23.6417236 | 43.3454393 |
| Chelsea Old church | 1712 | 1842 | alpha | 1.000092 | 1.000284 | 0.0083989 | 0.0083033 | 0.0082201 | 24055.1 | 0.0000095 | 0.95 | 0.0056545 | 0.0113658 |
| Chelsea Old church | 1712 | 1842 | beta | 1.000107 | 1.000363 | 0.0422444 | 0.0421520 | 0.0421527 | 20068.2 | 0.0000343 | 0.95 | 0.0327982 | 0.0517568 |
| Chelsea Old church | 1712 | 1842 | M | 1.000066 | 1.000214 | 50.2412943 | 50.4255236 | 50.6944550 | 32126.8 | 0.0173728 | 0.95 | 43.9580757 | 56.1242381 |
| St. Marylebone | 1742 | 1817 | alpha | 1.000026 | 1.000095 | 0.0125953 | 0.0125006 | 0.0123046 | 29334.6 | 0.0000102 | 0.95 | 0.0092608 | 0.0160318 |
| St. Marylebone | 1742 | 1817 | beta | 1.000017 | 1.000034 | 0.0420937 | 0.0420895 | 0.0423370 | 23957.1 | 0.0000291 | 0.95 | 0.0331445 | 0.0508272 |
| St. Marylebone | 1742 | 1817 | M | 1.000036 | 1.000085 | 40.5179648 | 40.7766676 | 41.3760128 | 31991.5 | 0.0170220 | 0.95 | 34.3796076 | 46.1332104 |
| St. Marylebone Paddington Street north | 1772 | 1853 | alpha | 1.000045 | 1.000166 | 0.0099037 | 0.0098127 | 0.0096774 | 27403.8 | 0.0000087 | 0.95 | 0.0071709 | 0.0127837 |
| St. Marylebone Paddington Street north | 1772 | 1853 | beta | 1.000055 | 1.000206 | 0.0488613 | 0.0488575 | 0.0485839 | 23270.2 | 0.0000301 | 0.95 | 0.0398523 | 0.0578266 |
| St. Marylebone Paddington Street north | 1772 | 1853 | M | 1.000039 | 1.000116 | 44.6690555 | 44.7919466 | 45.0496301 | 37001.7 | 0.0116510 | 0.95 | 40.1953904 | 48.9817326 |
| St. Bride’s lower churchyard | 1770 | 1849 | alpha | 1.000035 | 1.000073 | 0.0061790 | 0.0061316 | 0.0059751 | 14779.1 | 0.0000071 | 0.95 | 0.0045330 | 0.0078754 |
| St. Bride’s lower churchyard | 1770 | 1849 | beta | 1.000155 | 1.000339 | 0.0510752 | 0.0510280 | 0.0511331 | 11203.6 | 0.0000422 | 0.95 | 0.0423814 | 0.0598976 |
| St. Bride’s lower churchyard | 1770 | 1849 | M | 1.000130 | 1.000460 | 53.4368072 | 53.4511152 | 53.4536777 | 46992.7 | 0.0074618 | 0.95 | 50.2090353 | 56.5697935 |
| Sheen’s burial ground | 1763 | 1854 | alpha | 1.000091 | 1.000320 | 0.0129642 | 0.0128270 | 0.0124596 | 28565.8 | 0.0000128 | 0.95 | 0.0089230 | 0.0173233 |
| Sheen’s burial ground | 1763 | 1854 | beta | 1.000171 | 1.000495 | 0.0353994 | 0.0353305 | 0.0350479 | 24673.6 | 0.0000300 | 0.95 | 0.0262620 | 0.0446735 |
| Sheen’s burial ground | 1763 | 1854 | M | 1.000120 | 1.000420 | 39.9956498 | 40.5717091 | 41.5741951 | 29050.5 | 0.0299067 | 0.95 | 29.5817256 | 49.0658033 |
| Bow Baptist Church | 1816 | 1854 | alpha | 1.000037 | 1.000121 | 0.0177742 | 0.0176655 | 0.0171967 | 37363.4 | 0.0000114 | 0.95 | 0.0135868 | 0.0221462 |
| Bow Baptist Church | 1816 | 1854 | beta | 1.000013 | 1.000063 | 0.0344658 | 0.0344556 | 0.0344680 | 30272.0 | 0.0000249 | 0.95 | 0.0259810 | 0.0429301 |
| Bow Baptist Church | 1816 | 1854 | M | 1.000031 | 1.000063 | 30.6580796 | 31.3283020 | 32.6360138 | 33171.9 | 0.0277771 | 0.95 | 20.3999444 | 39.3695617 |
| St. Mary and St. Michael | 1843 | 1853 | alpha | 1.000523 | 1.001826 | 0.0186478 | 0.0185639 | 0.0182508 | 41699.1 | 0.0000099 | 0.95 | 0.0148267 | 0.0227130 |
| St. Mary and St. Michael | 1843 | 1853 | beta | 1.000441 | 1.001467 | 0.0402140 | 0.0402172 | 0.0404972 | 35162.0 | 0.0000216 | 0.95 | 0.0322916 | 0.0481568 |
| St. Mary and St. Michael | 1843 | 1853 | M | 1.000616 | 1.001944 | 30.8426109 | 31.1889790 | 31.6656994 | 38394.2 | 0.0171194 | 0.95 | 24.1587401 | 36.9724139 |
| St. Bride’s crypt (known age) | 1740 | 1853 | alpha | 1.001301 | 1.004385 | 0.0048650 | 0.0048100 | 0.0046364 | 11054.4 | 0.0000077 | 0.95 | 0.0033513 | 0.0064885 |
| St. Bride’s crypt (known age) | 1740 | 1853 | beta | 1.001527 | 1.004999 | 0.0492998 | 0.0492831 | 0.0490777 | 10841.1 | 0.0000350 | 0.95 | 0.0422819 | 0.0564716 |
| St. Bride’s crypt (known age) | 1740 | 1853 | M | 1.000820 | 1.002819 | 59.1168993 | 59.1961001 | 59.4409448 | 16528.6 | 0.0139187 | 0.95 | 55.5069567 | 62.4858268 |
| St. Bride’s crypt (estimates) | 1740 | 1853 | alpha | 1.000250 | 1.000942 | 0.0050511 | 0.0049857 | 0.0049500 | 13935.6 | 0.0000077 | 0.95 | 0.0033266 | 0.0068431 |
| St. Bride’s crypt (estimates) | 1740 | 1853 | beta | 1.000251 | 1.000919 | 0.0461973 | 0.0460966 | 0.0460772 | 11655.0 | 0.0000408 | 0.95 | 0.0375863 | 0.0548062 |
| St. Bride’s crypt (estimates) | 1740 | 1853 | M | 1.000110 | 1.000431 | 60.0918241 | 60.1324772 | 60.2370171 | 29765.3 | 0.0137390 | 0.95 | 55.4315320 | 64.7329115 |
kable(wellcome_result_r, caption = "London cemeteries data, corrected for population growth.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| cemetery | start | end | parameter | PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bermondsey Abbey | 1089 | 1538 | alpha | 1.0001999 | 1.0007416 | 0.0105288 | 0.0104025 | 0.0101065 | 26895.4 | 0.0000111 | 0.95 | 0.0071225 | 0.0141935 |
| Bermondsey Abbey | 1089 | 1538 | beta | 1.0003786 | 1.0010986 | 0.0429176 | 0.0429090 | 0.0434181 | 24113.7 | 0.0000308 | 0.95 | 0.0335341 | 0.0522185 |
| Bermondsey Abbey | 1089 | 1538 | M | 1.0001327 | 1.0004472 | 44.7061829 | 44.9293082 | 45.3226906 | 30386.5 | 0.0198385 | 0.95 | 37.7940665 | 51.2834230 |
| Bermondsey Abbey | 1089 | 1538 | rate | 1.0000303 | 1.0000756 | 0.0039098 | 0.0039108 | 0.0039733 | 106914.0 | 0.0000076 | 0.95 | -0.0009505 | 0.0088325 |
| St. Mary Graces | 1350 | 1540 | alpha | 1.0001410 | 1.0003568 | 0.0169749 | 0.0168588 | 0.0167558 | 33748.3 | 0.0000119 | 0.95 | 0.0128271 | 0.0213266 |
| St. Mary Graces | 1350 | 1540 | beta | 1.0000433 | 1.0001007 | 0.0372463 | 0.0372464 | 0.0370084 | 30177.8 | 0.0000242 | 0.95 | 0.0289760 | 0.0454249 |
| St. Mary Graces | 1350 | 1540 | M | 1.0001281 | 1.0002492 | 32.7675640 | 33.2209124 | 33.9417464 | 31746.8 | 0.0236912 | 0.95 | 24.2993787 | 40.4275089 |
| St. Mary Graces | 1350 | 1540 | rate | 1.0001305 | 1.0004837 | 0.0051616 | 0.0051627 | 0.0052870 | 100496.1 | 0.0000078 | 0.95 | 0.0003122 | 0.0100454 |
| St. Mary Hospital, 1120-1200 | 1120 | 1200 | alpha | 1.0000331 | 1.0001286 | 0.0228885 | 0.0227897 | 0.0226513 | 43799.9 | 0.0000115 | 0.95 | 0.0183155 | 0.0276638 |
| St. Mary Hospital, 1120-1200 | 1120 | 1200 | beta | 1.0000350 | 1.0001314 | 0.0379869 | 0.0379887 | 0.0379277 | 41935.6 | 0.0000186 | 0.95 | 0.0304787 | 0.0454167 |
| St. Mary Hospital, 1120-1200 | 1120 | 1200 | M | 1.0000459 | 1.0001549 | 24.9940336 | 25.4195077 | 26.1632091 | 39863.2 | 0.0202351 | 0.95 | 16.8860536 | 32.3216380 |
| St. Mary Hospital, 1120-1200 | 1120 | 1200 | rate | 1.0000328 | 1.0000475 | 0.0028308 | 0.0028305 | 0.0028200 | 115634.2 | 0.0000073 | 0.95 | -0.0021173 | 0.0076306 |
| St. Mary Hospital, 1200-1250 | 1200 | 1250 | alpha | 1.0000810 | 1.0003099 | 0.0230203 | 0.0229469 | 0.0229048 | 50830.0 | 0.0000094 | 0.95 | 0.0189207 | 0.0272159 |
| St. Mary Hospital, 1200-1250 | 1200 | 1250 | beta | 1.0001545 | 1.0005234 | 0.0398856 | 0.0398998 | 0.0399483 | 51029.8 | 0.0000157 | 0.95 | 0.0328956 | 0.0468336 |
| St. Mary Hospital, 1200-1250 | 1200 | 1250 | M | 1.0000928 | 1.0003558 | 25.5429589 | 25.8389492 | 26.4616904 | 46661.4 | 0.0149967 | 0.95 | 19.0144549 | 31.4789393 |
| St. Mary Hospital, 1200-1250 | 1200 | 1250 | rate | 1.0000406 | 1.0000908 | 0.0129320 | 0.0129281 | 0.0127274 | 107875.9 | 0.0000076 | 0.95 | 0.0080676 | 0.0177871 |
| St. Mary Hospital, 1250-1400 | 1250 | 1400 | alpha | 1.0000497 | 1.0001170 | 0.0184492 | 0.0184122 | 0.0182888 | 23215.0 | 0.0000084 | 0.95 | 0.0159587 | 0.0209832 |
| St. Mary Hospital, 1250-1400 | 1250 | 1400 | beta | 1.0000407 | 1.0001310 | 0.0588094 | 0.0588085 | 0.0589706 | 23589.8 | 0.0000177 | 0.95 | 0.0534970 | 0.0641442 |
| St. Mary Hospital, 1250-1400 | 1250 | 1400 | M | 1.0000497 | 1.0001156 | 31.6963826 | 31.7396954 | 31.8464384 | 24117.1 | 0.0070508 | 0.95 | 29.5007009 | 33.7824781 |
| St. Mary Hospital, 1250-1400 | 1250 | 1400 | rate | 0.9999962 | 0.9999989 | -0.0026207 | -0.0026209 | -0.0027932 | 56055.6 | 0.0000104 | 0.95 | -0.0073601 | 0.0022509 |
| St. Mary Hospital, 1400-1539 | 1400 | 1539 | alpha | 1.0000223 | 1.0000549 | 0.0231055 | 0.0230308 | 0.0230113 | 41925.6 | 0.0000104 | 0.95 | 0.0190097 | 0.0273502 |
| St. Mary Hospital, 1400-1539 | 1400 | 1539 | beta | 1.0000087 | 1.0000259 | 0.0399576 | 0.0399616 | 0.0400633 | 39732.1 | 0.0000178 | 0.95 | 0.0330820 | 0.0469712 |
| St. Mary Hospital, 1400-1539 | 1400 | 1539 | M | 1.0000141 | 1.0000391 | 25.4683995 | 25.7644549 | 26.3462367 | 38317.9 | 0.0165837 | 0.95 | 18.9737587 | 31.4815633 |
| St. Mary Hospital, 1400-1539 | 1400 | 1539 | rate | 1.0000340 | 1.0000951 | 0.0050553 | 0.0050563 | 0.0051778 | 103432.2 | 0.0000077 | 0.95 | 0.0001496 | 0.0098918 |
| New Churchyard | 1569 | 1739 | alpha | 1.0001279 | 1.0002871 | 0.0211766 | 0.0211136 | 0.0212054 | 37764.5 | 0.0000100 | 0.95 | 0.0174176 | 0.0249711 |
| New Churchyard | 1569 | 1739 | beta | 1.0000753 | 1.0001933 | 0.0400944 | 0.0400933 | 0.0400801 | 35294.2 | 0.0000185 | 0.95 | 0.0332312 | 0.0468600 |
| New Churchyard | 1569 | 1739 | M | 1.0001440 | 1.0003447 | 27.7108539 | 27.9722139 | 28.4872019 | 35217.0 | 0.0160479 | 0.95 | 21.6010226 | 33.2292167 |
| New Churchyard | 1569 | 1739 | rate | 1.0000620 | 1.0001365 | 0.0082621 | 0.0082646 | 0.0083576 | 87104.3 | 0.0000084 | 0.95 | 0.0033814 | 0.0131413 |
| St. Benet Sherehog | 1670 | 1740 | alpha | 1.0001805 | 1.0006101 | 0.0132861 | 0.0131411 | 0.0129458 | 34008.4 | 0.0000119 | 0.95 | 0.0091934 | 0.0176933 |
| St. Benet Sherehog | 1670 | 1740 | beta | 1.0001190 | 1.0003512 | 0.0381719 | 0.0381737 | 0.0382241 | 31530.9 | 0.0000266 | 0.95 | 0.0289791 | 0.0474535 |
| St. Benet Sherehog | 1670 | 1740 | M | 1.0002037 | 1.0006791 | 39.3972135 | 39.8401136 | 40.1526185 | 34591.5 | 0.0241655 | 0.95 | 30.3535344 | 47.6481468 |
| St. Benet Sherehog | 1670 | 1740 | rate | 1.0000344 | 1.0000931 | 0.0059873 | 0.0059983 | 0.0060528 | 119114.7 | 0.0000072 | 0.95 | 0.0011010 | 0.0108270 |
| Chelsea Old church | 1712 | 1842 | alpha | 1.0002873 | 1.0010299 | 0.0058789 | 0.0057818 | 0.0055736 | 24844.5 | 0.0000075 | 0.95 | 0.0036917 | 0.0082560 |
| Chelsea Old church | 1712 | 1842 | beta | 1.0002128 | 1.0007988 | 0.0472765 | 0.0472197 | 0.0472248 | 21617.0 | 0.0000341 | 0.95 | 0.0374445 | 0.0571072 |
| Chelsea Old church | 1712 | 1842 | M | 1.0001776 | 1.0006011 | 56.3070206 | 56.3582529 | 56.7461356 | 44134.7 | 0.0138780 | 0.95 | 50.5873981 | 62.0866861 |
| Chelsea Old church | 1712 | 1842 | rate | 1.0000451 | 1.0001660 | 0.0100601 | 0.0100643 | 0.0101297 | 89138.8 | 0.0000084 | 0.95 | 0.0051571 | 0.0149469 |
| St. Marylebone | 1742 | 1817 | alpha | 1.0000748 | 1.0001372 | 0.0095679 | 0.0094649 | 0.0091973 | 30628.4 | 0.0000087 | 0.95 | 0.0067098 | 0.0125807 |
| St. Marylebone | 1742 | 1817 | beta | 1.0000415 | 1.0001241 | 0.0459357 | 0.0459208 | 0.0457528 | 27451.1 | 0.0000277 | 0.95 | 0.0370076 | 0.0549197 |
| St. Marylebone | 1742 | 1817 | M | 1.0000736 | 1.0001274 | 46.1751078 | 46.2984132 | 46.3570171 | 40003.8 | 0.0136968 | 0.95 | 40.7083583 | 51.4616051 |
| St. Marylebone | 1742 | 1817 | rate | 1.0000683 | 1.0002323 | 0.0095688 | 0.0095712 | 0.0093581 | 99214.5 | 0.0000079 | 0.95 | 0.0047434 | 0.0145099 |
| St. Marylebone Paddington Street north | 1772 | 1853 | alpha | 1.0000358 | 1.0000900 | 0.0065801 | 0.0065013 | 0.0064360 | 29127.9 | 0.0000066 | 0.95 | 0.0044463 | 0.0087891 |
| St. Marylebone Paddington Street north | 1772 | 1853 | beta | 1.0001415 | 1.0004460 | 0.0544281 | 0.0544209 | 0.0547945 | 26218.3 | 0.0000292 | 0.95 | 0.0452271 | 0.0637787 |
| St. Marylebone Paddington Street north | 1772 | 1853 | M | 0.9999975 | 1.0000085 | 50.9632692 | 50.9739902 | 50.9618065 | 49233.1 | 0.0098106 | 0.95 | 46.6741737 | 55.2372052 |
| St. Marylebone Paddington Street north | 1772 | 1853 | rate | 1.0000364 | 1.0001074 | 0.0144206 | 0.0144255 | 0.0141691 | 101071.9 | 0.0000078 | 0.95 | 0.0094983 | 0.0192607 |
| St. Bride’s lower churchyard | 1770 | 1849 | alpha | 1.0011697 | 1.0042730 | 0.0037341 | 0.0036868 | 0.0036269 | 16620.6 | 0.0000049 | 0.95 | 0.0025631 | 0.0049982 |
| St. Bride’s lower churchyard | 1770 | 1849 | beta | 1.0015090 | 1.0051365 | 0.0582705 | 0.0582224 | 0.0580684 | 12836.2 | 0.0000410 | 0.95 | 0.0491681 | 0.0672636 |
| St. Bride’s lower churchyard | 1770 | 1849 | M | 1.0003029 | 1.0011116 | 59.3567949 | 59.3049875 | 59.1753323 | 40772.1 | 0.0095119 | 0.95 | 55.5901301 | 63.1117920 |
| St. Bride’s lower churchyard | 1770 | 1849 | rate | 1.0003038 | 1.0011395 | 0.0143225 | 0.0143172 | 0.0141355 | 52696.3 | 0.0000108 | 0.95 | 0.0094154 | 0.0191705 |
| Sheen’s burial ground | 1763 | 1854 | alpha | 1.0001549 | 1.0002068 | 0.0081112 | 0.0079857 | 0.0076079 | 28990.1 | 0.0000095 | 0.95 | 0.0051656 | 0.0113978 |
| Sheen’s burial ground | 1763 | 1854 | beta | 1.0000827 | 1.0001417 | 0.0418442 | 0.0418050 | 0.0417337 | 27930.4 | 0.0000294 | 0.95 | 0.0322170 | 0.0514367 |
| Sheen’s burial ground | 1763 | 1854 | M | 1.0001259 | 1.0001599 | 51.3035346 | 51.4719153 | 51.7458183 | 37127.6 | 0.0196709 | 0.95 | 43.8156221 | 58.7122226 |
| Sheen’s burial ground | 1763 | 1854 | rate | 1.0000471 | 1.0000606 | 0.0143440 | 0.0143429 | 0.0142681 | 101954.9 | 0.0000078 | 0.95 | 0.0093921 | 0.0191445 |
| Bow Baptist Church | 1816 | 1854 | alpha | 1.0000751 | 1.0002591 | 0.0110080 | 0.0109048 | 0.0107115 | 41439.7 | 0.0000082 | 0.95 | 0.0078878 | 0.0143335 |
| Bow Baptist Church | 1816 | 1854 | beta | 1.0000831 | 1.0003245 | 0.0409501 | 0.0409441 | 0.0407475 | 36617.2 | 0.0000234 | 0.95 | 0.0322211 | 0.0497674 |
| Bow Baptist Church | 1816 | 1854 | M | 1.0000690 | 1.0002060 | 44.0086393 | 44.2046299 | 44.6069317 | 46933.1 | 0.0152560 | 0.95 | 37.4300374 | 50.3741413 |
| Bow Baptist Church | 1816 | 1854 | rate | 1.0000216 | 1.0000239 | 0.0174851 | 0.0174851 | 0.0173758 | 106259.5 | 0.0000076 | 0.95 | 0.0125967 | 0.0223740 |
| St. Mary and St. Michael | 1843 | 1853 | alpha | 1.0001563 | 1.0005720 | 0.0122807 | 0.0121938 | 0.0120196 | 46093.7 | 0.0000074 | 0.95 | 0.0092409 | 0.0154457 |
| St. Mary and St. Michael | 1843 | 1853 | beta | 1.0002253 | 1.0007624 | 0.0459562 | 0.0459699 | 0.0456100 | 42613.3 | 0.0000202 | 0.95 | 0.0378149 | 0.0541866 |
| St. Mary and St. Michael | 1843 | 1853 | M | 1.0001425 | 1.0005089 | 40.6794124 | 40.8054593 | 41.3726101 | 51800.7 | 0.0109648 | 0.95 | 35.7481079 | 45.5245164 |
| St. Mary and St. Michael | 1843 | 1853 | rate | 1.0000407 | 1.0001181 | 0.0176425 | 0.0176439 | 0.0178219 | 111336.5 | 0.0000075 | 0.95 | 0.0128415 | 0.0226355 |
| St. Bride’s crypt (known age) | 1740 | 1853 | alpha | 11.3187848 | 26.7160198 | 0.0062628 | 0.0058303 | 0.0034420 | 1.5 | 0.0018915 | 0.95 | 0.0031442 | 0.0102527 |
| St. Bride’s crypt (known age) | 1740 | 1853 | beta | 11.7161168 | 22.9647008 | 0.0510415 | 0.0510591 | 0.0509381 | 1.4 | 0.0034864 | 0.95 | 0.0443241 | 0.0572525 |
| St. Bride’s crypt (known age) | 1740 | 1853 | M | 11.7488400 | 23.5976438 | 53.9513110 | 54.4984270 | 54.3621152 | 1.4 | 4.7419679 | 0.95 | 44.8901900 | 62.3280593 |
| St. Bride’s crypt (known age) | 1740 | 1853 | rate | 1.0001302 | 1.0004858 | -0.9898864 | -0.9898864 | -0.9898825 | 68206.5 | 0.0000004 | 0.95 | -0.9900793 | -0.9896890 |
| St. Bride’s crypt (estimates) | 1740 | 1853 | alpha | 1.0010883 | 1.0036469 | 0.8089951 | 0.8096464 | 0.8091857 | 3141.3 | 0.0003460 | 0.95 | 0.7708209 | 0.8467743 |
| St. Bride’s crypt (estimates) | 1740 | 1853 | beta | 1.0011031 | 1.0035351 | 0.0049692 | 0.0049308 | 0.0048867 | 3152.0 | 0.0000121 | 0.95 | 0.0036820 | 0.0063247 |
| St. Bride’s crypt (estimates) | 1740 | 1853 | M | 1.0008190 | 1.0029237 | -1038.5780551 | -1022.5151667 | -1000.6858905 | 3228.3 | 3.1452459 | 0.95 | -1405.8300586 | -716.0579775 |
| St. Bride’s crypt (estimates) | 1740 | 1853 | rate | 1.0000235 | 1.0000707 | -0.9873975 | -0.9873961 | -0.9874078 | 123992.2 | 0.0000071 | 0.95 | -0.9922468 | -0.9824618 |
Figure 6: Modal ages from historical and osteological data
source("./chapter_04_results/english_wellcome.R")
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
plot(modal_ages_plot)
Table 2: Overview of modelled osteological data from London cemeteries
The data overview is build during pre-processing in ./chapter_04_results/Wellcome_DB.R and saved to a textfile (sep = \t).
wellcome_overview_all
kable(wellcome_overview_all, caption = "London cemeteries overview.") %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| cemetery | beta | beta_range | M | M_range | ex20 | ex25 | beta | beta_range | M | M_range | ex20 | ex25 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bermondsey Abbey | 0.0414 | 0.0319-0.0504 | 42.6 | 34.7-48.4 | 25.5 | 22.7 | 0.0434 | 0.0335-0.0522 | 45.3 | 37.8-51.3 | 26.8 | 23.8 |
| Bow Baptist Church | 0.0345 | 0.026-0.0429 | 32.6 | 20.4-39.4 | 22.7 | 20.4 | 0.0407 | 0.0322-0.0498 | 44.6 | 37.4-50.4 | 27.1 | 24.2 |
| Chelsea Old church | 0.0422 | 0.0328-0.0518 | 50.7 | 44-56.1 | 30.4 | 27.3 | 0.0472 | 0.0374-0.0571 | 56.7 | 50.6-62.1 | 33.9 | 30.4 |
| New Churchyard | 0.0365 | 0.0299-0.0432 | 22.5 | 13.7-27.9 | 17.0 | 15.0 | 0.0401 | 0.0332-0.0469 | 28.5 | 21.6-33.2 | 18.3 | 16.1 |
| Sheen’s burial ground | 0.0350 | 0.0263-0.0447 | 41.6 | 29.6-49.1 | 27.3 | 24.6 | 0.0417 | 0.0322-0.0514 | 51.7 | 43.8-58.7 | 31.8 | 28.6 |
| St. Benet Sherehog | 0.0353 | 0.0265-0.0446 | 36.1 | 23.6-43.3 | 23.7 | 21.2 | 0.0382 | 0.029-0.0475 | 40.2 | 30.4-47.6 | 25.3 | 22.7 |
| St. Bride’s crypt (estimates) | 0.0461 | 0.0376-0.0548 | 60.2 | 55.4-64.7 | 36.4 | 32.8 | 0.0049 | 0.0037-0.0063 | -1000.7 | -1405.8–716.1 | 1.2 | 1.2 |
| St. Bride’s crypt (known age) | 0.0491 | 0.0423-0.0565 | 59.4 | 55.5-62.5 | 35.7 | 32.0 | 0.0509 | 0.0443-0.0573 | 54.4 | 44.9-62.3 | 39.3 | 35.4 |
| St. Bride’s lower churchyard | 0.0511 | 0.0424-0.0599 | 53.5 | 50.2-56.6 | 31.0 | 27.5 | 0.0581 | 0.0492-0.0673 | 59.2 | 55.6-63.1 | 34.8 | 30.9 |
| St. Mary Graces | 0.0349 | 0.0267-0.0427 | 29.1 | 17.8-36.2 | 20.8 | 18.6 | 0.0370 | 0.029-0.0454 | 33.9 | 24.3-40.4 | 22.2 | 19.8 |
| St. Mary Hospital, 1120-1200 | 0.0366 | 0.0289-0.0437 | 23.6 | 12.9-29.7 | 17.4 | 15.4 | 0.0379 | 0.0305-0.0454 | 26.2 | 16.9-32.3 | 18.1 | 16.0 |
| St. Mary Hospital, 1200-1250 | 0.0355 | 0.0289-0.0424 | 17.8 | 7.7-24.3 | 15.7 | 13.8 | 0.0399 | 0.0329-0.0468 | 26.5 | 19-31.5 | 17.5 | 15.3 |
| St. Mary Hospital, 1250-1400 | 0.0577 | 0.0529-0.0634 | 32.0 | 30-33.6 | 16.0 | 13.4 | 0.0590 | 0.0535-0.0641 | 31.8 | 29.5-33.8 | 15.7 | 13.1 |
| St. Mary Hospital, 1400-1539 | 0.0374 | 0.0307-0.0443 | 22.2 | 13.7-27.8 | 16.7 | 14.7 | 0.0401 | 0.0331-0.047 | 26.3 | 19-31.5 | 17.4 | 15.2 |
| St. Mary and St. Michael | 0.0405 | 0.0323-0.0482 | 31.7 | 24.2-37 | 20.0 | 17.6 | 0.0456 | 0.0378-0.0542 | 41.4 | 35.7-45.5 | 23.6 | 20.8 |
| St. Marylebone | 0.0423 | 0.0331-0.0508 | 41.4 | 34.4-46.1 | 24.5 | 21.7 | 0.0458 | 0.037-0.0549 | 46.4 | 40.7-51.5 | 27.2 | 24.1 |
| St. Marylebone Paddington Street north | 0.0486 | 0.0399-0.0578 | 45.0 | 40.2-49 | 25.4 | 22.4 | 0.0548 | 0.0452-0.0638 | 51.0 | 46.7-55.2 | 28.5 | 25.0 |
Marylebone.R
Data are hard coded in the code. Sources: Miles et al. (2008b), 97–103 table 32 (St Marylebone); Henderson et al. (2015), 81 (St Marylebone north of Paddington street)
source("./lifetables_processing/Marylebone.R")
kable(Marylebone_ranges, caption = "St Marylebone, corrected with population growth rate of 2.75 per-cent.") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| parameter | modes | HDI.ranges |
|---|---|---|
| Marylebone beta | 0.0526 | 0.0435-0.0618 |
| Marylebone M | 54.2470 | 49.5-59.3 |
| Marylebone north beta | 0.0588 | 0.0496-0.0682 |
| Marylebone north M | 55.6570 | 51.3-59.9 |
Figure 7: St. Bride’s Crypt. Density of actual ages and Bayesian model of Gompertz distribution of actual ages and osteological estimates (without correction for population growth).
The plot is build in ./lifetables_processing/stbrides_crypt.R within
the if-statement on runCodeNew (s. data limitations
above).
plot(stbrides_crypt_plot)
Figure 8: Simulation of population increase with known age-at-death and Maximum Likelihood Estimation (MLE) (top four) and osteological estimates, Bayesian model and including rate of increase (bottom four).
source("./chapter_04_results/simulations_pop_incr_run.R")
The chapter ‘Supporting informations’ provides details about the London cemeteries included in the study.
Calculation of the lowest \(\beta\)-value for any of the Coale & Demeny life tables (Coale/Demeny (1983)) which is 0.0391 (the female table “West”, level 1).
source("./chapter_supplement/coale_demeny_life_tables_gompertz.R")
min(gompertz_df$Gompertz_shape)
## [1] 0.03913138
Simulations for evaluation of algorithms for retrieving Gompertz parameters. The file “./chapter_supplement/simulations_run.R” provides various tests and plots from the evaluation process. The validity of the algorithms is tested via root mean square error (RMSE) of between expected and estimated values for Gompertz \(\beta\).
Figure S1: Comparing expected and estimated Gompertz \(\beta\)-values by different algorithms with known age-at-death (n = 1,000).
source("./chapter_supplement/simulations_run.R")
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
gridExtra::grid.arrange(grobs = plot_list_shapes, ncol = 3)
Figure S2: Difference between expected and estimated Gompertz \(\beta\)-values by different algorithms with known age-at-death (n = 1,000).
source("./chapter_supplement/simulations_run.R")
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
gridExtra::grid.arrange(grobs = plot_list_diff, ncol = 3)
Table S1: Root mean square errors (RMSE) for different formulas for fitting known age-at-death, ordered ascendingly.
# table of RMSEs
kable(rmse_result[order(rmse_result$RMSE) ,], caption = "Evaluation of algorithms via RMSE.") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| method | RMSE | NAs | |
|---|---|---|---|
| 11 | Bayes (5y-cat) | 0.0041953 | 0 |
| 10 | Bayes | 0.0042255 | 0 |
| 4 | survival | 0.0042981 | 0 |
| 7 | MLE | 0.0043000 | 0 |
| 12 | Bayes (10y-cat) | 0.0043487 | 0 |
| 8 | MLE (5y-cat) | 0.0043686 | 0 |
| 9 | MLE (10y-cat) | 0.0045265 | 0 |
| 5 | survival (5y-cat) | 0.0046064 | 0 |
| 1 | OLS | 0.0049051 | 519 |
| 3 | WNLS | 0.0053132 | 16 |
| 2 | WOLS | 0.0057136 | 0 |
| 6 | survival (10y-cat) | 0.0065228 | 0 |
| 13 | Bayes poisson | 0.0106965 | 0 |
Figure S3: Comparing expected and estimated Gompertz \(\beta\)-values by different algorithms with estimated age-at-death (n = 1,000).
source("./chapter_supplement/simulations_run.R")
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
gridExtra::grid.arrange(grobs = plot_list_estim_shapes, ncol = 2)
Table S2: Root mean square errors (RMSE) for different formulas for fitting estimated age-at-death, ordered ascendingly.
# table of RMSEs
kable(rmse_estim_result[order(rmse_estim_result$RMSE) ,], caption = "Evaluation of algorithms via RMSE for estimated age-at-death.") %>%
kableExtra::kable_styling(latex_options = "HOLD_position")
| method | RMSE | NAs | |
|---|---|---|---|
| 8 | MLE_wo_OL | 0.0128521 | 18 |
| 6 | Bayes (cat) | 0.0137203 | 0 |
| 1 | OLS | 0.0237398 | 95 |
| 3 | WNLS | 0.0260833 | 9 |
| 2 | WOLS | 0.0276202 | 0 |
| 5 | MLE (cat) | 0.0302704 | 0 |
| 7 | Bayes poisson | 0.0599111 | 0 |
| 4 | survival (cat) | 0.1454623 | 0 |
Figure S4: Detailed plot for the Bayesian model of expected Gompertz \(\beta\)-values (left) and sample size (right) vs. difference of expected/estimated Gompertz \(\beta\)-values.
#source("./chapter_supplement/simulations_run.R")
gridExtra::grid.arrange(grobs = plot_list_bayes_diff, ncol = 2)
Show that means are stable in Bayesian modelling, regardless of the number of MCMC-steps.
source("./chapter_supplement/bayes_complete.R") # can take a few minutes
kable (bayes_complete, caption = paste0("Bayesian model with simulated dataset and different number of steps. n = ",
n, ", Gompertz beta = ", round(beta, 4), ".", sep = "")) %>%
kableExtra::kable_styling(latex_options = c("HOLD_position","scale_down"))
| mode | thinning | steps | parameter | PSRF Point est. | PSRF Upper C.I. | Mean | Median | Mode | ESS | MCSE | HDImass | HDIlow | HDIhigh |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| known_age | 1 | 10000 | a | 1.003210 | 1.006108 | 0.0028582 | 0.0028441 | 0.0027725 | 462.7 | 0.0000154 | 0.95 | 0.0022403 | 0.0035193 |
| known_age | 1 | 10000 | b | 1.001893 | 1.003920 | 0.0480363 | 0.0480265 | 0.0481745 | 488.6 | 0.0000947 | 0.95 | 0.0440097 | 0.0520917 |
| known_age | 1 | 10000 | M | 1.001259 | 1.003216 | 73.8375371 | 73.8501409 | 73.6934420 | 930.5 | 0.0357533 | 0.95 | 71.6915433 | 75.9608132 |
| known_age | 20 | 100000 | a | 1.000011 | 1.000109 | 0.0028495 | 0.0028327 | 0.0027934 | 71982.2 | 0.0000013 | 0.95 | 0.0022163 | 0.0035260 |
| known_age | 20 | 100000 | b | 1.000005 | 1.000090 | 0.0480993 | 0.0480962 | 0.0483082 | 71181.0 | 0.0000080 | 0.95 | 0.0438344 | 0.0521777 |
| known_age | 20 | 100000 | M | 1.000000 | 1.000078 | 73.8543153 | 73.8768307 | 73.9884330 | 84071.3 | 0.0037849 | 0.95 | 71.6339091 | 75.9294081 |
| estimation | 1 | 10000 | a | 1.007384 | 1.023678 | 0.0028312 | 0.0028026 | 0.0027942 | 167.5 | 0.0000382 | 0.95 | 0.0019049 | 0.0038193 |
| estimation | 1 | 10000 | b | 1.011691 | 1.038693 | 0.0510970 | 0.0508290 | 0.0503803 | 86.5 | 0.0005942 | 0.95 | 0.0404465 | 0.0624583 |
| estimation | 1 | 10000 | M | 1.005548 | 1.017117 | 71.9242579 | 71.9119671 | 72.0531786 | 392.2 | 0.1119194 | 0.95 | 67.6950056 | 76.3291669 |
| estimation | 20 | 100000 | a | 1.000247 | 1.000941 | 0.0027769 | 0.0027509 | 0.0027034 | 29177.9 | 0.0000026 | 0.95 | 0.0019290 | 0.0036726 |
| estimation | 20 | 100000 | b | 1.000354 | 1.001342 | 0.0516959 | 0.0514776 | 0.0502964 | 20843.0 | 0.0000356 | 0.95 | 0.0421542 | 0.0619696 |
| estimation | 20 | 100000 | M | 1.000091 | 1.000334 | 71.8362699 | 71.7754410 | 71.6155191 | 45976.8 | 0.0102799 | 0.95 | 67.6297829 | 76.2104655 |
Institute for Pre- and Proto History - Kiel University nils.mueller-scheessel@ufg.uni-kiel.de↩︎
Institute of Clinical Molecular Biology - Kiel University, k.fuchs@ikmb.uni-kiel.de↩︎
Institute for Pre- and Proto History - Kiel University, crinne@ufg.uni-kiel.de↩︎